Showing papers on "Symmetry (physics) published in 1974"
Book•
01 Jan 1974
TL;DR: In this article, a phenomenological theory of magnetic order impurities and alloys external fields electrons, phonons, and transport aspects of the electron-electron interaction is presented.
Abstract: Electronic structure lattice dynamics symmetry and its consequences phenomenological theories of magnetic order impurities and alloys external fields electrons, phonons, and transport aspects of the electron-electron interaction.
832 citations
TL;DR: In this paper, the O(N) generalization of the σ model in the limit of large N, for four, three, two, and one space-time dimensions, was studied.
Abstract: We study the O(N) generalization of the σ model in the limit of large N, for four, three, two, and one space-time dimensions. We compute the effective potential and some momentum-dependent Green's functions. In one and two dimensions, spontaneous symmetry breakdown is impossible; any asymmetric minimum inserted in the tree-approximation potential is immediately filled in by the effects of radiative corrections. This is in agreement with general theorems. In four dimensions, the model is inconsistent; it possesses a tachyon. In three dimensions, the model seems to be consistent, and offers an interesting example of some nonlinear effects associated with spontaneous symmetry breakdown that are not present in the usual (tree-approximation) models.
303 citations
TL;DR: A method for constructing some of the unitary irreducible representations of the Wess-Zumino super-gauge symmetry is given in this paper, which is used in the analysis of S -matrix elements.
130 citations
92 citations
TL;DR: Multi stationary states of prescribed symmetries in a sixteen-cell network are found and their stability with respect to symmetric disturbances is examined by means of elementary concentration patterns—a “symmetry-adapted basis”—and their interaction properties are described.
89 citations
85 citations
TL;DR: In this article, a new numerical method for use in the solution of classical equations of motion is described, accurate to third order in the coordinates and second-order in the velocities, which has the unique property of preserving the energy and total linear and angular momenta at their initial values in the computation.
80 citations
12 Jun 1974
TL;DR: The application of symmetry analysis to uniform waveguides is discussed in this article, where the authors provide exact information concerning mode classification, mode degeneracy, modal electromagnetic field symmetries, and the minimum waveguide sectors which completely determine the modes in each mode class.
Abstract: The application of symmetry analysis to uniform waveguides is discussed. Symmetry analysis provides exact information concerning mode classification, mode degeneracy, modal electromagnetic- field symmetries, and the minimum waveguide sectors which completely determine the modes in each mode class. This paper provides a summary of the development. that leads to the results concerning symmetry-induced modal characteristics of uniform waveguides discussed in the previous paper. Some of the concepts of group theory are introduced, including the irreducible representations of symmetry groups. The use of the irreducible representations to determine the mode classes and their degeneracies is described. The projection operators belonging to the irreducible representations are introduced and their application to determining the azimuthal symmetry of the modal fields is explained. The minimum waveguide sectors for the mode classes are obtained from the azimuthal symmetry of the modal fields.
62 citations
TL;DR: In this article, the existence of triangle anomalies requires that some of the symmetry currents must have well-defined gauge transformation properties, and exact low-energy theorems for certain matrix elements of the divergences of the currents are established to all orders in perturbation theory.
TL;DR: In this paper, the authors discuss the linearization stability of the initial-value constraints and make no statements about the dynamical stability of these constraints, and show that all closed solutions for which the intrinsic geometry possesses a conformal symmetry are incomplete, but stable.
Abstract: We discuss the completeness and "linearization stability" of the initial-value constraints. We show that all closed solutions for which the intrinsic geometry possesses a conformal symmetry are incomplete, but stable. All closed, vacuum, moment-of-time symmetry solutions are incomplete, but only the flat case is unstable. This particular incompleteness vanishes on the addition of any source field. All other closed solutions to the initial-value constraints for which the trace of the momentum is a covariant constant are complete and stable except those solutions where the metric and the momentum have the same exact symmetry. All such closed, vacuum solutions are unstable. All asymptotically flat maximal solutions are complete and stable. In this paper we treat only the linearization stability of the initial-value constraints and make no statements about the dynamical stability of the solutions.
TL;DR: In this article, it was shown that for gauge theories with perturbative spontaneous symmetry breakdown, the question of invariance is solely settled by the structure of the quantum corrections to the classical scalar potential.
Abstract: For gauge theories with perturbative spontaneous symmetry breakdown it may happen that the question of $\mathrm{CP}$ invariance is solely settled by the structure of the quantum corrections to the classical scalar potential. It is shown that this can occur if and only if there exist spinless bosons which are massless in the tree aproximation and which are non-Goldstone modes. This can be achieved in a natural way (in the technical sense) if an accidental symmetry is present. The general theorem is illustrated with a few formal examples, some of which yield $\mathrm{CP}$ invariance and some $\mathrm{CP}$ violation. Our theorem also implies that if the leading radiative corrections opt for $\mathrm{CP}$ invariance, then the theory is $\mathrm{CP}$-invariant to all orders. Our examples further reveal the possibility that some gross features of the particle spectrum may also be solely determined by quantum effects.
TL;DR: The closest we can come to a unified view of nature is a description in terms of elementary particles and their mutual interactions as discussed by the authors, and there is no serious reason to doubt its existence.
Abstract: O ne of man's enduring hopes has been to find a few simple general laws that would explain why na ture, with all its seeming complexity and variety, is the way it is. At the present moment the closest we can come to a unified view of nature is a description in terms of elementary particles and their mutual interactions. All ordinary matter is composed of just those elementary par ticles that happen to possess both mass and (relative) stability: the electron, the proton and the neutron. To these must be added the particles of zero mass: the photon, or quantum of electromagnetic radiation, the neutrino, which plays an essential role in certain kinds of radio activity, and the graviton, or quantum of gravitational radiation. (The graviton interacts too weakly with matter for it to have been observed yet, but there is no serious reason to doubt its existence.) A few additional short-lived particles can be found in cosmic rays, and with par ticle accelerators we can create a vast number of even shorter-lived species [see top illustration on page 52]. Although the various particles differ Widely in mass, charge, lifetime and in other ways, they all share two attributes that qualify them as being \"elementary.\" First, as far as we know, any two par ticles of the same species are, except for their position and state of motion, abso lutely identical, whether they occupy the same atom or lie at opposite ends of the universe. Second, there is not now any successful theory that explains the ele mentary particles in terms of more ele mentary constituents, in the sense that the atomic nucleus is understood to be composed of protons and neutrons and the atom is understood to be composed of a nucleus and electrons. It is true that
TL;DR: In this article, the calculus of variations is used to derive the torque equations, the solutions of which are found by relaxation methods on a digital computer, and with the aid of Maxwell's equations to predict the observed optical patterns, including the case of magnetic fields applied along the symmetry axis.
Abstract: Elasticity theory is applied to nematic liquid crystals with particular boundary conditions. The calculus of variations is used to derive the torque equations, the solutions of which are found by relaxation methods on a digital computer. These solutions are used to draw pictures of the molecular arrangements and with the aid of Maxwell's equations to predict the observed optical patterns, including the case of magnetic fields applied along the symmetry axis.
TL;DR: In this paper, it was shown that it is always possible to find a bilinear form that makes a given linear operator symmetric, and that a variational formulation requires the symmetry of the operator.
TL;DR: In this article, the authors exploit the knowledge of the Racah algebra for the higher unitary groups to give a general formula for the partial widths for the direct product subgroup U ( N k )× U (k) of the full unitary group U(N) of a given shell model vector space.
TL;DR: In this article, the symmetry condition for a first-order Stark effect of a molecular rovibronic level is considered for cases in which hyperfine splittings are negligible and there are no accidental degeneracies.
TL;DR: The theory of the determination of the irreducible representations of the two-dimensional space groups is briefly reviewed in this article, and then it is used to produce tables for each of the 2D space groups.
TL;DR: In this paper, the construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space-time is discussed, and a possible choice of Lagrangian for the gauge fields is presented.
Abstract: The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincare group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.
Journal Article•
TL;DR: In this article, the basic principles of the two different schools of thought on buckling theory (rotary symmetric theories and non-symmetric theories) are discussed, and some asymmetric buckling formulae giving design examples of the steel-lined pressure shafts for the Matucana power plant in Peru and the Hornberg project in Switzerland.
Abstract: Having discussed the basic principles of the two different schools of thought on buckling theory (rotary symmetric theories and non-symmetric theories), the author proposes some asymmetric buckling formulae giving design examples of the steel-lined pressure shafts for the Matucana power plant in Peru and the Hornberg project in Switzerland. The last part of the article gives formulae for ring-stiffened pipes. /TRRL/
TL;DR: In this article, it was shown that it is always possible to expand the scattering matrix for an isotropic medium in generalized spherical functions, and that the symmetry properties of the scattering process give rise to simple symmetry relations for the expansion coefficents.
Abstract: It is shown that it is always possible to expand the scattering matrix for an isotropic medium in generalized spherical functions. Additional physical symmetry properties of the scattering process, e.g., time-reversal invariance or reflection invariance, give rise to simple symmetry relations for the expansion coefficents. The expansion in generalized spherical functions naturally leads to decomposition of variables and appears to be the simplest way to include the various symmetry relations for the scattering matrix discussed in the literature.
TL;DR: A new interpretation of thermodynamics is presented in this article, which is the study of those properties of macroscopic matter that follow from the symmetry properties of physical laws mediated through the statistics of large systems.
Abstract: A new interpretation of thermodynamics is advanced; thermodynamics is the study of those properties of macroscopic matter that follow from the symmetry properties of physical laws, mediated through the statistics of large systems.
TL;DR: In this article, it was shown from the field equations that a body admitting an arbitrary symmetry must satisfy an integral condition analogous to the equilibrium criterion, and it was proved that the vanishing of the scalar curvature of the associated space implies the flatness of the space-time metric.
Abstract: The stationary gravitational equations in vacuum are expressed in five different forms. A necessary integral condition on the twist potential φ is derived. The Papapetrou‐Ehlers class of stationary solutions is rederived in a different way. In the study of the complex potential theory it is proved from the field equations that a body admitting an arbitrary symmetry must satisfy an integral condition analogous to the equilibrium criterion. It is proved that the vanishing of the scalar curvature of the associated space implies the flatness of the space‐time metric. A proof is given for the fact that the only analytic functions of the complex potential F which preserve the field equations form a four‐parameter Mobius group. It is also shown that any differentiable function of F and F which preserves the field equations must either be an analytic function of F or the conjugate of such a function. Next the conformastationary vacuum metrics are classified. In the study of the axially symmetric stationary field...
TL;DR: In this paper, the peculiarities of the scalarS ≡Rijkl Rijkl are exhibited for two axially-symmetric static (Weyl) gravitational fields.
Abstract: The peculiarities of the scalarS ≡RijklRijkl are exhibited for two axially-symmetric static (Weyl) gravitational fields. By examiningS along curved families of trajectories to the Weyl singularities, examples are found which contradict previous claims by Gautreau and Anderson regarding ‘directional singularities’. Proper circumferences about the Bach and Weyl line-mass singularity are also examined. There is no apparent correlation between the source structure and the behaviour ofS from this analysis.
TL;DR: The state of polarization of light generated at the three wave mixing frequency ω3 = 2ω1 − ω2 is observed in a few simple geometries, demonstrating a deviation from Kleinman's symmetry in cubic crystals as mentioned in this paper.